Cellular materials are often used as impact/blast attenuators due to their capacity to absorb kinetic energy when compressed to large strains. For such applications, three key material properties are the crushing stress, plateau stress and densification strain. The difficulties associated with obtaining these mechanical properties from dynamic/impact tests are outlined. The results of an experimental investigation of the quasi-static and dynamic mechanical properties of two types of cellular materials are reported.The dynamic tests were carried out using Hopkinson pressure bars. Experimentally determined propagation coefficients are employed to represent both dispersion and attenuation effects as stress waves travel along the bars. Propagation coefficients were determined for 20 mm and 40 mm diameter viscoelastic PMMA pressure bars and for elastic Magnesium pressure bars. The use of the elementary wave theory is shown to give satisfactory results for frequencies of up to approximately 15 kHz, 8 kHz and 30 kHz for the 20 mm and 40 mm diameter PMMA bars and the 23 mm diameter Magnesium bars respectively. The use of low impedance, viscoelastic pressure bars is shown to be preferable for testing low density, low strength materials.The quasi-static and dynamic compressive properties of balsa wood, Rohacell-51WF and Rohacell-110WF foams are investigated along all three principal directions. The dynamic properties were investigated by performing Split Hopkinson Pressure Bar (SHPB) and Direct Impact (DI) tests. In general, the crushing stress, the plateau stress and the densification strain remain constant with increasing strain rate of the SHPB tests. However, a dynamic enhancement of the crushing stress and plateau stress was revealed for balsa wood and Rohacell-51WF. In contrast, the plateau stresses of the Rohacell-110WF specimens are lower for SHPB than quasi-static tests. From the DI tests, it is shown that compaction waves have negligible effect on the stresses during dynamic compaction of along and across the grain balsa wood at impact speeds between approximately 20-100 m/s. Alternatively, the proximal end stresses of both Rohacell-51WF and 110WF foams increase with increasing impact velocity, following the quadratic trend predicted by 'shock theory'. This indicates that compaction waves are important for the case of Rohacell foam, even at low impact velocities.